ist denke ich der übliche Ausdruck

Es kommt, denke ich, wie immer auf den Kontext an. In Pressemitteilungen etc. dürfte "Headquarters" angebracht sein; in einem Vertrag oder anderen juristisch relevanten Texten nicht ;-)

I've seen and used : "The company's headquarters is registered in CITY."

The company is headquartered in X
The company has its head office in X
The company' central headquarters are in X

...just some possibilities

As Bacon says, context is the key. In UK contracts that would be the company's 'registered office'.

RRR, thanks for the support. One question though: I thought that a company's principal place of business need not necessarily be the same as the place of the registered office. That true?

Yes, that's true. So understanding one's context becomes even more important. In a contract the 'registered office' tends to be the all-important address, as this is per se 'registered' and can be kept track of, while any other premises can be bought and sold with no record of this necessarily being 'registered' with any official body or advised to the other party (i.e. if the other party had only given you a trading address and not their registered office address and they 'did a runner', you might have great difficulty tracking them down).

But to cut a long story short, yes, 'principal place of business' and 'registered office' are not always one and the same place.